find the eq to the graph for the horizontal asymtote of y= 3 - x+b/x-c

my guess is that it would be 2 b/c bringing the 3 to the other side would make it -1. and -x over x is also -1 is this right?

yes.

To find the equation of the horizontal asymptote of a rational function, we need to analyze the behavior of the function as x approaches positive and negative infinity.

In the given function, y = (3 - x + b) / (x - c), notice that both the numerator and denominator are linear functions of x. To determine the horizontal asymptote, we can compare the degrees of the numerator and denominator.

The degree of the numerator is 1 (since it is a linear function) and the degree of the denominator is also 1. When the degrees of the numerator and denominator are the same, the horizontal asymptote is a line with the equation y = a, where a is the ratio of the leading coefficients.

In this case, the leading coefficient of the numerator is -1 (the coefficient of x), and the leading coefficient of the denominator is 1. Therefore, the equation of the horizontal asymptote is y = (-1) / 1 = -1.

So, your guess that the equation of the horizontal asymptote is y = -1 is correct, not 2. The fraction -x / x simplifies to -1, not 2.

Please note that the value of b and c does not affect the equation of the horizontal asymptote as they cancel out when simplifying the function.